clifford_a-_pickover_surfing_through_hyperspacebookfi-org

236 addendum
Many of you are probably asking: what is outside the universe? The
answer is unclear. I must reiterate that this question supposes that the ultimate
physical reality must be a Euclidean space of some dimension. That is,
it presumes that if space is a hypersphere, then the hypersphere must sit in a
four-dimensional Euclidean space, allowing us to view it from the outside.
As the authors of the Scientific American article point out, nature need not
adhere to this notion. It would be perfectly acceptable for the universe to be
a hypersphere and not be embedded in any higher-dimensional space. We
have difficulty visualizing this because we are used to viewing shapes from
the outside. But there need not be an "outside."
As many papers have been published on cosmic topology in the past three
years as in the preceding 80. Today, cosmologists are poised to determine the
topology of our universe through observation. For example, if we look out
into space, and images of the same galaxy are seen to repeat on rectangular
lattice points, this will suggest we live in a 3-torus. (Your standard 2-torus, or
doughnut shape, is built from a curved square, while a 3-torus is built from a
cube.) Sadly, Finding such patterns would be difficult because the images of a
galaxy would depict different points in time. Astronomers would need to be
able to recognize the same galaxy at different points in its history.
One of the most difficult ideas to grasp concerning cosmic topology is
how a hyperbolic space can be finite. For more information on this and
other topics in cosmic topology, see: Jean-Pierre Luminet, Glenn D. Starkman,
and Jeffrey R. Weeks, "Is space infinite?" Scientific American, April
280(4): 90-97, 1999